Extreme velocity gradients in turbulent flows

Buaria, Dhawal; Pumir, Alain; Bodenschatz, Eberhard; Yeung, P. K.

doi:10.1088/1367-2630/ab0756

Cited by 110 publications

(214 citation statements)

References 47 publications

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“…6,7,25,26 Other previous studies visualize isosurfaces whose values are determined based on mean values of variables. 27,28 Table 2 shows ω and found that f (0.98) is very close to f (2.9rms) . Table 2 EL .…”

Section: Irrotational Straining Motion Rigid-body Rotation and Sheamentioning

confidence: 79%

Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

et al. 2020

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The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor ∇u is decomposed into three components representing an irrotational straining motion (∇u) EL , a rigid-body rotation (∇u) RR , and a shearing motion (∇u) SH . Strength of these motions can be quantified with the decomposed components. A procedure of the triple decomposition is proposed for three-dimensional flows, where the decomposition is applied in a basic reference frame identified by examining a finite number of reference frames obtained by three sequential rotational transformations of a Cartesian coordinate. Even though more than one basic reference frame may be available for the triple decomposition, the results of the decomposition depend little on the choice of basic reference frame. In homogeneous isotropic turbulence, regions with strong rigid-body rotations or straining motions are highly intermittent in space, while most flow regions exhibit moderately ✩ Accepted for publication. https://doi.

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Section: Irrotational Straining Motion Rigid-body Rotation and Sheamentioning

confidence: 79%

Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

et al. 2020

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“…It has been shown in several previous studies that A 2 exhibits a heavy-tailed pdf, characteristic of intermittency [32,33]. It has further been shown that in the conventionally used decomposition, enstrophy exhibits a pdf with a wider tail and is more intermittent than dissipation [2,3]. The pdfs of VG magnitude and its triple decomposition constituents are plotted in Fig.…”

Section: A Composition Of Vg Magnitudementioning

confidence: 88%

“…This decomposition has led to important insight into small-scale intermittency [1][2][3], intense structures in turbulence [4][5][6][7] and local streamline geometry [8][9][10]. However, recent studies [11][12][13] have shown that strain-rate and vorticity do not clearly identify the presence of normal-straining and rigid-body-rotation of the fluid.…”

Section: Introductionmentioning

confidence: 99%

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Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

Das

Girimaji

2020

New J. Phys.

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Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor (Aij) into the symmetric strain-rate (Sij) and anti-symmetric rotationrate (Wij) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate (Nij), pure-shear (Hij) and rigid-body-rotation-rate (Rij). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants space. Using DNS data sets of forced isotropic turbulence, the velocitygradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude (A 2 ). Especially, shear contribution is dominant in regions of intermittency (high values of A 2 ). It is also shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the absence of intermittency of the pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence. *

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“…We emphasise that the small-scale fluid-velocity fluctuations in turbulence are universal [63] but not Gaussian, contrary to the statistics assumed in the statistical model. The non-Gaussian character increases as the Reynolds number increases [64]. Nevertheless, earlier comparisons between results from the statistical model and DNS often show a qualitative or even quantitative agreement [10,48,53,[65][66][67].…”

Section: Statistical Modelmentioning

confidence: 95%

Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence

et al. 2019

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We study the angular dynamics of small non-spherical particles settling in a turbulent flow, such as ice crystals in clouds, aggregates of organic material in the oceans, or fibres settling in turbulent pipe flow. Most solid particles encountered in Nature are not spherical, and their orientations affect their settling speeds, as well as their collision and aggregation rates in suspensions. Whereas the random action of turbulent eddies favours an isotropic distribution of orientations, gravitational settling breaks the rotational symmetry. The precise nature of the symmetry breaking, however, is subtle. We demonstrate here that the fluid-inertia torque plays a dominant role in the problem. As a consequence rod-like particles tend to settle in turbulence with horizontal orientation, the more so the larger the settling number Sv (a dimensionless measure of the settling speed). For large Sv we determine the fluctuations around this preferential horizontal orientation for prolate particles with arbitrary aspect ratios, assuming small Stokes number St (a dimensionless measure of particle inertia). Our theory is based on a statistical model representing the turbulent velocity fluctuations by Gaussian random functions. This overdamped theory predicts that the orientation distribution is very narrow at large Sv, with a variance proportional to -Sv 4 . By considering the role of particle inertia, we analyse the limitations of the overdamped theory, and determine its range of applicability. Our predictions are in excellent agreement with numerical simulations of simplified models of turbulent flows. Finally we contrast our results with those of an alternative theory predicting that the orientation variance is proportional to -Sv 2 at large Sv.

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Extreme velocity gradients in turbulent flows

Cited by 110 publications

References 47 publications

Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence

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